Thread: Math Puzzle - need help quick

My math teacher gave us this puzzle with the promise of "something special" if we figured it out. I've tried, but I just cant figure it out and its giving me a headache! Anyone that can help me would be greatly appreciated.

The Puzzle:

"A Mathematician was early on his way to work one day and decided to figure out how many possible ways he could get to work. Help the mathematician figure out how many possible routes there are from START to FINISH. You may only move to the right and cannot go backwards. If you reach a fork, you can take the top or bottom path.

Thanks in advance to anyone who can help

Let's see, Plato may show up and set us straight.

There are 6 steps from beginning to end and 3 across. If our start is (0,0), then the end would have step (6,3)

A block walker gets to (n,k) from either corner (n-1,k) or (n-1,k-1)

To get to corner (6,3) we go to (5,3) and goes left to (6,3) or goes to (5,2) and turns right to (6,3).

Thus the number of routes is (n-1,k-1)+(n-1,k)

It does seem rather large, but thanks anyways

I think it is the parts of the puzzle where only one path leads away that gives us both troubles.

I got far enough to figure that when you start, you have a choice of two paths, at the end of those you also have a choice of two paths, giving you a total of 4 possible paths to get past the first diamond. From there, there are also two paths off of each of the four paths, which equals 8 possible paths to get to the center.

From there, I am completely lost.

EDIT: For some reason, there was a different post above, which I replied to...

Odd. Anyways, thanks for your help galactus, that does make sense

Hi putrobi,

Yes that was mine which I deleted because it was clearly rubbish. Sorry for the trouble I caused.

Ok, makes sense. Thanks anyways

Originally Posted by putrobi

My math teacher gave us this puzzle with the promise of "something special" if we figured it out. I've tried, but I just cant figure it out and its giving me a headache! Anyone that can help me would be greatly appreciated.

The Puzzle:

"A Mathematician was early on his way to work one day and decided to figure out how many possible ways he could get to work. Help the mathematician figure out how many possible routes there are from START to FINISH. You may only move to the right and cannot go backwards. If you reach a fork, you can take the top or bottom path.

Thanks in advance to anyone who can help

The two high-lighted conditions do not go together.

You may only move to the right and cannot go backwards.
So at the start you can only move along the bottom path. You are not allowed to try the top path because that would be moving to the left.

Then you reach a fork. And your dead there.
You cannot move anymore because you are not allowed to go backwards.
You cannot go along the top path there because that would be going left. And you cannot also choose the bottom path because that would be going straight ahead...not going right.

I think the conditions are OK. It seems to be the same question as this.